Subjects algebra

Missing Money

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Missing Money


1. **State the problem:** Three girls paid $100 each, totaling $300, for a motel room. The correct charge was $250, so the clerk gave $50 to the attendant to return to the girls. The attendant gave $10 back to each girl ($30 total) and kept $20. The girls effectively paid $270 ($90 each), and the attendant has $20. The question is: where is the missing $10? 2. **Analyze the payments:** - Total initially paid: $300 - Correct room cost: $250 - Amount returned to girls: $30 ($10 each) - Amount kept by attendant: $20 3. **Calculate the actual money flow:** - Girls paid $300 initially. - They got back $30, so net payment by girls is $300 - $30 = $270. - Out of this $270, $250 went to the motel, $20 went to the attendant. 4. **Clarify the confusion:** The mistake is in adding the $20 (attendant's money) to the $270 (girls' net payment). Instead, the $270 already includes the $20 kept by the attendant. 5. **Correct accounting:** $$ \text{Girls' net payment} = 270 = 250 + 20 $$ The $250 is the motel's charge, and $20 is the attendant's tip. 6. **Conclusion:** There is no missing $10. The error is in adding the $20 to the $270 instead of subtracting the $30 returned to the girls. **Final answer:** The missing $10 is a result of incorrect addition; the $270 already includes the $20 kept by the attendant, so no money is missing.